Exponentials Lesson 6 Episode 2 (Teachers)

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In this episode, Josh and Arobindo are challenged to make sense of the equation 3^3/4 =. First, they are asked to explain why the height of the beanstalk at Day ¾ can be written as both 3^3/4 and  [1:57]. Later they are asked to make sense of why the fourth root of 3 is cubed [3:34]. This takes some careful explanation. Eventually Josh and Arobindo identify two related ideas: the fourth root of 3 comes from equally partitioning the growth factor of 3 into four equal parts and the cubing comes from multiplying that smaller growth factor by itself three times.

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 1:56] Compare the two expressions 3^3/4 and . What does each expression mean in the context of the growing beanstalk? Do you prefer one representation over the other? Is one expression more appropriate for the context? 
2. [Pause the video at 4:12] Summarize Arobindo’s explanation for why  works to describe the height of the beanstalk on Day ¾. Explain what the fourth root of 3 means in the beanstalk context and what the power of 3 means in the context. 

After watching the video, ask students to summarize the video in their own words. This is also a good opportunity to ask your students to tell a partner something they’ve come to understand about roots and something they still might be wondering about or are confused by.